LMFDB - Embedded newform 74.8.b.a.73.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(73,74)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.14
Character	$\chi$	$=$	74.73
Dual form			74.8.b.a.73.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000i q^{2} -61.7342 q^{3} -64.0000 q^{4} -552.363i q^{5} -493.873i q^{6} +606.238 q^{7} -512.000i q^{8} +1624.11 q^{9} +4418.91 q^{10} -1574.05 q^{11} +3950.99 q^{12} -6183.12i q^{13} +4849.91i q^{14} +34099.7i q^{15} +4096.00 q^{16} +17764.7i q^{17} +12992.9i q^{18} -34251.9i q^{19} +35351.3i q^{20} -37425.6 q^{21} -12592.4i q^{22} -76896.1i q^{23} +31607.9i q^{24} -226980. q^{25} +49465.0 q^{26} +34749.7 q^{27} -38799.3 q^{28} +46583.6i q^{29} -272798. q^{30} -17681.9i q^{31} +32768.0i q^{32} +97173.0 q^{33} -142118. q^{34} -334864. i q^{35} -103943. q^{36} +(-26300.5 + 306986. i) q^{37} +274015. q^{38} +381710. i q^{39} -282810. q^{40} -465753. q^{41} -299405. i q^{42} +594996. i q^{43} +100740. q^{44} -897097. i q^{45} +615169. q^{46} -470646. q^{47} -252863. q^{48} -456018. q^{49} -1.81584e6i q^{50} -1.09669e6i q^{51} +395720. i q^{52} -7937.52 q^{53} +277998. i q^{54} +869450. i q^{55} -310394. i q^{56} +2.11451e6i q^{57} -372669. q^{58} +1.46340e6i q^{59} -2.18238e6i q^{60} +1.76239e6i q^{61} +141456. q^{62} +984596. q^{63} -262144. q^{64} -3.41533e6 q^{65} +777384. i q^{66} -2.34359e6 q^{67} -1.13694e6i q^{68} +4.74712e6i q^{69} +2.67891e6 q^{70} +2.45676e6 q^{71} -831543. i q^{72} +437865. q^{73} +(-2.45588e6 - 210404. i) q^{74} +1.40124e7 q^{75} +2.19212e6i q^{76} -954252. q^{77} -3.05368e6 q^{78} -2.26054e6i q^{79} -2.26248e6i q^{80} -5.69717e6 q^{81} -3.72603e6i q^{82} +9.71016e6 q^{83} +2.39524e6 q^{84} +9.81257e6 q^{85} -4.75997e6 q^{86} -2.87580e6i q^{87} +805916. i q^{88} -8.74504e6i q^{89} +7.17678e6 q^{90} -3.74845e6i q^{91} +4.92135e6i q^{92} +1.09158e6i q^{93} -3.76517e6i q^{94} -1.89195e7 q^{95} -2.02291e6i q^{96} +1.59186e7i q^{97} -3.64815e6i q^{98} -2.55643e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30}+ \cdots - 53279900 q^{99}+O(q^{100}) $ 24 * q - 106 * q^3 - 1536 * q^4 + 104 * q^7 + 17554 * q^9 + 1136 * q^10 + 366 * q^11 + 6784 * q^12 + 98304 * q^16 - 239820 * q^21 - 675570 * q^25 + 97008 * q^26 + 338780 * q^27 - 6656 * q^28 + 350400 * q^30 - 763792 * q^33 + 713632 * q^34 - 1123456 * q^36 + 41652 * q^37 - 30816 * q^38 - 72704 * q^40 + 1729722 * q^41 - 23424 * q^44 - 488496 * q^46 + 114756 * q^47 - 434176 * q^48 + 4003056 * q^49 - 1115964 * q^53 - 2075632 * q^58 + 3248208 * q^62 - 2350900 * q^63 - 6291456 * q^64 - 5246556 * q^65 - 2717994 * q^67 - 5649440 * q^70 + 10643280 * q^71 - 10450370 * q^73 - 1064064 * q^74 - 17737980 * q^75 + 11665236 * q^77 + 8431856 * q^78 + 47300176 * q^81 + 555912 * q^83 + 15348480 * q^84 - 4853096 * q^85 - 12070464 * q^86 + 32064160 * q^90 - 58516956 * q^95 - 53279900 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			8.00000i			0.707107i
$2$			8.00000i			0.707107i
$3$	−61.7342			−1.32008			−0.660041	−	0.751229i	$-0.729461\pi$
$3$	−61.7342			−1.32008			−0.660041	+	0.751229i	$0.729461\pi$
$4$	−64.0000			−0.500000
$5$		−	552.363i		−	1.97620i	−0.153827	−	0.988098i	$-0.549160\pi$
$5$		−	552.363i		−	1.97620i	0.153827	−	0.988098i	$-0.450840\pi$
$6$		−	493.873i		−	0.933440i
$7$	606.238			0.668037			0.334018	−	0.942567i	$-0.391595\pi$
$7$	606.238			0.668037			0.334018	+	0.942567i	$0.391595\pi$
$8$		−	512.000i		−	0.353553i
$9$	1624.11			0.742619
$10$	4418.91			1.39738
$11$	−1574.05			−0.356571			−0.178285	−	0.983979i	$-0.557055\pi$
$11$	−1574.05			−0.356571			−0.178285	+	0.983979i	$0.557055\pi$
$12$	3950.99			0.660041
$13$		−	6183.12i		−	0.780560i	−0.920696	−	0.390280i	$-0.872378\pi$
$13$		−	6183.12i		−	0.780560i	0.920696	−	0.390280i	$-0.127622\pi$
$14$			4849.91i			0.472373i
$15$			34099.7i			2.60874i
$16$	4096.00			0.250000
$17$			17764.7i			0.876974i	0.898738	+	0.438487i	$0.144485\pi$
$17$			17764.7i			0.876974i	−0.898738	+	0.438487i	$0.855515\pi$
$18$			12992.9i			0.525111i
$19$		−	34251.9i		−	1.14564i	−0.819682	−	0.572819i	$-0.805850\pi$
$19$		−	34251.9i		−	1.14564i	0.819682	−	0.572819i	$-0.194150\pi$
$20$			35351.3i			0.988098i
$21$	−37425.6			−0.881864
$22$		−	12592.4i		−	0.252133i
$23$		−	76896.1i		−	1.31782i	−0.752220	−	0.658911i	$-0.771017\pi$
$23$		−	76896.1i		−	1.31782i	0.752220	−	0.658911i	$-0.228983\pi$
$24$			31607.9i			0.466720i
$25$	−226980.			−2.90535
$26$	49465.0			0.551939
$27$	34749.7			0.339765
$28$	−38799.3			−0.334018
$29$			46583.6i			0.354683i	0.984149	+	0.177341i	$0.0567497\pi$
$29$			46583.6i			0.354683i	−0.984149	+	0.177341i	$0.943250\pi$
$30$	−272798.			−1.84466
$31$		−	17681.9i		−	0.106602i	−0.998579	−	0.0533008i	$-0.983026\pi$
$31$		−	17681.9i		−	0.106602i	0.998579	−	0.0533008i	$-0.0169742\pi$
$32$			32768.0i			0.176777i
$33$	97173.0			0.470703
$34$	−142118.			−0.620114
$35$		−	334864.i		−	1.32017i
$36$	−103943.			−0.371309
$37$	−26300.5	+	306986.i	−0.0853608	+	0.996350i
$37$	−26300.5	+	306986.i	−0.0853608	+	0.996350i
$38$	274015.			0.810088
$39$			381710.i			1.03040i
$40$	−282810.			−0.698691
$41$	−465753.			−1.05539			−0.527694	−	0.849434i	$-0.676943\pi$
$41$	−465753.			−1.05539			−0.527694	+	0.849434i	$0.676943\pi$
$42$		−	299405.i		−	0.623572i
$43$			594996.i			1.14123i	0.821216	+	0.570617i	$0.193296\pi$
$43$			594996.i			1.14123i	−0.821216	+	0.570617i	$0.806704\pi$
$44$	100740.			0.178285
$45$		−	897097.i		−	1.46756i
$46$	615169.			0.931842
$47$	−470646.			−0.661228			−0.330614	−	0.943766i	$-0.607256\pi$
$47$	−470646.			−0.661228			−0.330614	+	0.943766i	$0.607256\pi$
$48$	−252863.			−0.330021
$49$	−456018.			−0.553727
$50$		−	1.81584e6i		−	2.05439i
$51$		−	1.09669e6i		−	1.15768i
$52$			395720.i			0.390280i
$53$	−7937.52			−0.00732351			−0.00366176	−	0.999993i	$-0.501166\pi$
$53$	−7937.52			−0.00732351			−0.00366176	+	0.999993i	$0.501166\pi$
$54$			277998.i			0.240250i
$55$			869450.i			0.704653i
$56$		−	310394.i		−	0.236187i
$57$			2.11451e6i			1.51234i
$58$	−372669.			−0.250799
$59$			1.46340e6i			0.927644i	0.885928	+	0.463822i	$0.153522\pi$
$59$			1.46340e6i			0.927644i	−0.885928	+	0.463822i	$0.846478\pi$
$60$		−	2.18238e6i		−	1.30437i
$61$			1.76239e6i			0.994141i	0.867710	+	0.497071i	$0.165591\pi$
$61$			1.76239e6i			0.994141i	−0.867710	+	0.497071i	$0.834409\pi$
$62$	141456.			0.0753788
$63$	984596.			0.496096
$64$	−262144.			−0.125000
$65$	−3.41533e6			−1.54254
$66$			777384.i			0.332837i
$67$	−2.34359e6			−0.951964			−0.475982	−	0.879455i	$-0.657907\pi$
$67$	−2.34359e6			−0.951964			−0.475982	+	0.879455i	$0.657907\pi$
$68$		−	1.13694e6i		−	0.438487i
$69$			4.74712e6i			1.73964i
$70$	2.67891e6			0.933502
$71$	2.45676e6			0.814627			0.407314	−	0.913288i	$-0.366466\pi$
$71$	2.45676e6			0.814627			0.407314	+	0.913288i	$0.366466\pi$
$72$		−	831543.i		−	0.262555i
$73$	437865.			0.131738			0.0658689	−	0.997828i	$-0.479018\pi$
$73$	437865.			0.131738			0.0658689	+	0.997828i	$0.479018\pi$
$74$	−2.45588e6	−	210404.i	−0.704526	−	0.0603592i
$75$	1.40124e7			3.83530
$76$			2.19212e6i			0.572819i
$77$	−954252.			−0.238202
$78$	−3.05368e6			−0.728605
$79$		−	2.26054e6i		−	0.515842i	−0.966166	−	0.257921i	$-0.916963\pi$
$79$		−	2.26054e6i		−	0.515842i	0.966166	−	0.257921i	$-0.0830374\pi$
$80$		−	2.26248e6i		−	0.494049i
$81$	−5.69717e6			−1.19114
$82$		−	3.72603e6i		−	0.746272i
$83$	9.71016e6			1.86403			0.932015	−	0.362419i	$-0.118049\pi$
$83$	9.71016e6			1.86403			0.932015	+	0.362419i	$0.118049\pi$
$84$	2.39524e6			0.440932
$85$	9.81257e6			1.73307
$86$	−4.75997e6			−0.806974
$87$		−	2.87580e6i		−	0.468211i
$88$			805916.i			0.126067i
$89$		−	8.74504e6i		−	1.31491i	−0.753493	−	0.657456i	$-0.771633\pi$
$89$		−	8.74504e6i		−	1.31491i	0.753493	−	0.657456i	$-0.228367\pi$
$90$	7.17678e6			1.03772
$91$		−	3.74845e6i		−	0.521443i
$92$			4.92135e6i			0.658911i
$93$			1.09158e6i			0.140723i
$94$		−	3.76517e6i		−	0.467559i
$95$	−1.89195e7			−2.26400
$96$		−	2.02291e6i		−	0.233360i
$97$			1.59186e7i			1.77095i	0.464691	+	0.885473i	$0.346165\pi$
$97$			1.59186e7i			1.77095i	−0.464691	+	0.885473i	$0.653835\pi$
$98$		−	3.64815e6i		−	0.391544i
$99$	−2.55643e6			−0.264796
$100$	1.45267e7			1.45267
$101$	1.91415e7			1.84863			0.924317	−	0.381625i	$-0.124635\pi$
$101$	1.91415e7			1.84863			0.924317	+	0.381625i	$0.124635\pi$
$102$	8.77351e6			0.818602
$103$		−	1.57904e7i		−	1.42384i	−0.702258	−	0.711922i	$-0.747825\pi$
$103$		−	1.57904e7i		−	1.42384i	0.702258	−	0.711922i	$-0.252175\pi$
$104$	−3.16576e6			−0.275970
$105$			2.06725e7i			1.74273i
$106$		−	63500.2i		−	0.00517850i
$107$	−5.51837e6			−0.435479			−0.217740	−	0.976007i	$-0.569868\pi$
$107$	−5.51837e6			−0.435479			−0.217740	+	0.976007i	$0.569868\pi$
$108$	−2.22398e6			−0.169882
$109$			1.02306e7i			0.756676i	0.925668	+	0.378338i	$0.123504\pi$
$109$			1.02306e7i			0.756676i	−0.925668	+	0.378338i	$0.876496\pi$
$110$	−6.95560e6			−0.498265
$111$	1.62364e6	−	1.89515e7i	0.112683	−	1.31526i
$112$	2.48315e6			0.167009
$113$		−	6.79737e6i		−	0.443166i	−0.975142	−	0.221583i	$-0.928878\pi$
$113$		−	6.79737e6i		−	0.443166i	0.975142	−	0.221583i	$-0.0711224\pi$
$114$	−1.69161e7			−1.06938
$115$	−4.24746e7			−2.60428
$116$		−	2.98135e6i		−	0.177341i
$117$		−	1.00421e7i		−	0.579658i
$118$	−1.17072e7			−0.655943
$119$			1.07696e7i			0.585851i
$120$	1.74590e7			0.922330
$121$	−1.70095e7			−0.872857
$122$	−1.40991e7			−0.702964
$123$	2.87529e7			1.39320
$124$			1.13164e6i			0.0533008i
$125$			8.22223e7i			3.76534i
$126$			7.87677e6i			0.350793i
$127$	−4.08913e7			−1.77140			−0.885702	−	0.464255i	$-0.846322\pi$
$127$	−4.08913e7			−1.77140			−0.885702	+	0.464255i	$0.846322\pi$
$128$		−	2.09715e6i		−	0.0883883i
$129$		−	3.67316e7i		−	1.50652i
$130$		−	2.73227e7i		−	1.09074i
$131$			1.72757e7i			0.671408i	0.941968	+	0.335704i	$0.108974\pi$
$131$			1.72757e7i			0.671408i	−0.941968	+	0.335704i	$0.891026\pi$
$132$	−6.21907e6			−0.235351
$133$		−	2.07648e7i		−	0.765328i
$134$		−	1.87487e7i		−	0.673140i
$135$		−	1.91945e7i		−	0.671441i
$136$	9.09553e6			0.310057
$137$	2.64899e7			0.880153			0.440076	−	0.897960i	$-0.354951\pi$
$137$	2.64899e7			0.880153			0.440076	+	0.897960i	$0.354951\pi$
$138$	−3.79769e7			−1.23011
$139$	−8.09392e6			−0.255627			−0.127814	−	0.991798i	$-0.540796\pi$
$139$	−8.09392e6			−0.255627			−0.127814	+	0.991798i	$0.540796\pi$
$140$			2.14313e7i			0.660085i
$141$	2.90549e7			0.872876
$142$			1.96541e7i			0.576029i
$143$			9.73258e6i			0.278325i
$144$	6.65234e6			0.185655
$145$	2.57311e7			0.700922
$146$			3.50292e6i			0.0931526i
$147$	2.81519e7			0.730966
$148$	1.68323e6	−	1.96471e7i	0.0426804	−	0.498175i
$149$	−5.49381e7			−1.36057			−0.680286	−	0.732947i	$-0.738144\pi$
$149$	−5.49381e7			−1.36057			−0.680286	+	0.732947i	$0.738144\pi$
$150$			1.12100e8i			2.71197i
$151$	1.48904e7			0.351955			0.175978	−	0.984394i	$-0.443691\pi$
$151$	1.48904e7			0.351955			0.175978	+	0.984394i	$0.443691\pi$
$152$	−1.75370e7			−0.405044
$153$			2.88518e7i			0.651257i
$154$		−	7.63402e6i		−	0.168434i
$155$	−9.76686e6			−0.210666
$156$		−	2.44294e7i		−	0.515202i
$157$	−4.18076e7			−0.862197			−0.431098	−	0.902305i	$-0.641874\pi$
$157$	−4.18076e7			−0.862197			−0.431098	+	0.902305i	$0.641874\pi$
$158$	1.80843e7			0.364755
$159$	490016.			0.00966764
$160$	1.80998e7			0.349345
$161$		−	4.66174e7i		−	0.880354i
$162$		−	4.55773e7i		−	0.842260i
$163$		−	9.23734e7i		−	1.67067i	−0.549743	−	0.835334i	$-0.685274\pi$
$163$		−	9.23734e7i		−	1.67067i	0.549743	−	0.835334i	$-0.314726\pi$
$164$	2.98082e7			0.527694
$165$		−	5.36748e7i		−	0.930201i
$166$			7.76813e7i			1.31807i
$167$		−	7.61039e6i		−	0.126444i	−0.997999	−	0.0632222i	$-0.979862\pi$
$167$		−	7.61039e6i		−	0.126444i	0.997999	−	0.0632222i	$-0.0201377\pi$
$168$			1.91619e7i			0.311786i
$169$	2.45175e7			0.390726
$170$			7.85006e7i			1.22547i
$171$		−	5.56288e7i		−	0.850772i
$172$		−	3.80798e7i		−	0.570617i
$173$	−3.47700e7			−0.510556			−0.255278	−	0.966868i	$-0.582167\pi$
$173$	−3.47700e7			−0.510556			−0.255278	+	0.966868i	$0.582167\pi$
$174$	2.30064e7			0.331075
$175$	−1.37604e8			−1.94088
$176$	−6.44733e6			−0.0891426
$177$		−	9.03418e7i		−	1.22457i
$178$	6.99603e7			0.929783
$179$			4.27579e7i			0.557225i	0.960404	+	0.278612i	$0.0898745\pi$
$179$			4.27579e7i			0.557225i	−0.960404	+	0.278612i	$0.910126\pi$
$180$			5.74142e7i			0.733780i
$181$	−1.23217e8			−1.54453			−0.772263	−	0.635303i	$-0.780875\pi$
$181$	−1.23217e8			−1.54453			−0.772263	+	0.635303i	$0.780875\pi$
$182$	2.99876e7			0.368716
$183$		−	1.08800e8i		−	1.31235i
$184$	−3.93708e7			−0.465921
$185$	1.69568e8	+	1.45274e7i	1.96898	+	0.168690i
$186$	−8.73264e6			−0.0995062
$187$		−	2.79626e7i		−	0.312703i
$188$	3.01213e7			0.330614
$189$	2.10666e7			0.226975
$190$		−	1.51356e8i		−	1.60089i
$191$			1.31163e8i			1.36205i	0.732260	+	0.681025i	$0.238465\pi$
$191$			1.31163e8i			1.36205i	−0.732260	+	0.681025i	$0.761535\pi$
$192$	1.61832e7			0.165010
$193$		−	8.55596e7i		−	0.856679i	−0.903618	−	0.428339i	$-0.859099\pi$
$193$		−	8.55596e7i		−	0.856679i	0.903618	−	0.428339i	$-0.140901\pi$
$194$	−1.27349e8			−1.25225
$195$	2.10843e8			2.03628
$196$	2.91852e7			0.276864
$197$	8.65321e7			0.806390			0.403195	−	0.915114i	$-0.367900\pi$
$197$	8.65321e7			0.806390			0.403195	+	0.915114i	$0.367900\pi$
$198$		−	2.04515e7i		−	0.187239i
$199$			8.49061e7i			0.763754i	0.924213	+	0.381877i	$0.124722\pi$
$199$			8.49061e7i			0.763754i	−0.924213	+	0.381877i	$0.875278\pi$
$200$			1.16214e8i			1.02720i
$201$	1.44680e8			1.25667
$202$			1.53132e8i			1.30718i
$203$			2.82408e7i			0.236941i
$204$			7.01881e7i			0.578839i
$205$			2.57265e8i			2.08565i
$206$	1.26323e8			1.00681
$207$		−	1.24888e8i		−	0.978640i
$208$		−	2.53261e7i		−	0.195140i
$209$			5.39144e7i			0.408501i
$210$	−1.65380e8			−1.23230
$211$	2.25603e8			1.65332			0.826660	−	0.562701i	$-0.190238\pi$
$211$	2.25603e8			1.65332			0.826660	+	0.562701i	$0.190238\pi$
$212$	508001.			0.00366176
$213$	−1.51666e8			−1.07538
$214$		−	4.41470e7i		−	0.307930i
$215$	3.28654e8			2.25530
$216$		−	1.77919e7i		−	0.120125i
$217$		−	1.07195e7i		−	0.0712138i
$218$	−8.18451e7			−0.535051
$219$	−2.70312e7			−0.173905
$220$		−	5.56448e7i		−	0.352327i
$221$	1.09841e8			0.684531
$222$	1.51612e8	+	1.29891e7i	0.930033	+	0.0796791i
$223$	−1.53872e8			−0.929165			−0.464583	−	0.885530i	$-0.653796\pi$
$223$	−1.53872e8			−0.929165			−0.464583	+	0.885530i	$0.653796\pi$
$224$			1.98652e7i			0.118093i
$225$	−3.68640e8			−2.15757
$226$	5.43790e7			0.313366
$227$		−	5.56054e7i		−	0.315520i	−0.987477	−	0.157760i	$-0.949573\pi$
$227$		−	5.56054e7i		−	0.315520i	0.987477	−	0.157760i	$-0.0504272\pi$
$228$		−	1.35329e8i		−	0.756168i
$229$	7.53531e7			0.414645			0.207323	−	0.978273i	$-0.433525\pi$
$229$	7.53531e7			0.414645			0.207323	+	0.978273i	$0.433525\pi$
$230$		−	3.39797e8i		−	1.84150i
$231$	5.89100e7			0.314447
$232$	2.38508e7			0.125399
$233$	−1.89539e8			−0.981642			−0.490821	−	0.871260i	$-0.663303\pi$
$233$	−1.89539e8			−0.981642			−0.490821	+	0.871260i	$0.663303\pi$
$234$	8.03364e7			0.409880
$235$			2.59967e8i			1.30672i
$236$		−	9.36576e7i		−	0.463822i
$237$			1.39552e8i			0.680954i
$238$	−8.61571e7			−0.414259
$239$		−	2.47866e8i		−	1.17442i	−0.809433	−	0.587212i	$-0.800226\pi$
$239$		−	2.47866e8i		−	1.17442i	0.809433	−	0.587212i	$-0.199774\pi$
$240$			1.39672e8i			0.652185i
$241$		−	3.52141e7i		−	0.162053i	−0.996712	−	0.0810266i	$-0.974180\pi$
$241$		−	3.52141e7i		−	0.162053i	0.996712	−	0.0810266i	$-0.0258199\pi$
$242$		−	1.36076e8i		−	0.617203i
$243$	2.75712e8			1.23263
$244$		−	1.12793e8i		−	0.497071i
$245$			2.51888e8i			1.09427i
$246$			2.30023e8i			0.985141i
$247$	−2.11784e8			−0.894239
$248$	−9.05315e6			−0.0376894
$249$	−5.99448e8			−2.46067
$250$	−6.57778e8			−2.66250
$251$		−	2.88357e8i		−	1.15099i	−0.817804	−	0.575497i	$-0.804809\pi$
$251$		−	2.88357e8i		−	1.15099i	0.817804	−	0.575497i	$-0.195191\pi$
$252$	−6.30141e7			−0.248048
$253$			1.21039e8i			0.469897i
$254$		−	3.27130e8i		−	1.25257i
$255$	−6.05771e8			−2.28780
$256$	1.67772e7			0.0625000
$257$			2.29423e8i			0.843085i	0.906809	+	0.421543i	$0.138511\pi$
$257$			2.29423e8i			0.843085i	−0.906809	+	0.421543i	$0.861489\pi$
$258$	2.93853e8			1.06527
$259$	−1.59444e7	+	1.86106e8i	−0.0570241	+	0.665598i
$260$	2.18581e8			0.771270
$261$			7.56567e7i			0.263394i
$262$	−1.38206e8			−0.474757
$263$	−4.68491e8			−1.58802			−0.794010	−	0.607905i	$-0.792010\pi$
$263$	−4.68491e8			−1.58802			−0.794010	+	0.607905i	$0.792010\pi$
$264$		−	4.97526e7i		−	0.166419i
$265$			4.38440e6i			0.0144727i
$266$	1.66119e8			0.541168
$267$			5.39868e8i			1.73579i
$268$	1.49990e8			0.475982
$269$	−5.58160e7			−0.174834			−0.0874170	−	0.996172i	$-0.527861\pi$
$269$	−5.58160e7			−0.174834			−0.0874170	+	0.996172i	$0.527861\pi$
$270$	1.53556e8			0.474781
$271$	−8.92064e7			−0.272272			−0.136136	−	0.990690i	$-0.543468\pi$
$271$	−8.92064e7			−0.272272			−0.136136	+	0.990690i	$0.543468\pi$
$272$			7.27642e7i			0.219243i
$273$			2.31407e8i			0.688347i
$274$			2.11919e8i			0.622362i
$275$	3.57280e8			1.03596
$276$		−	3.03816e8i		−	0.869818i
$277$		−	6.08294e8i		−	1.71963i	−0.510608	−	0.859814i	$-0.670580\pi$
$277$		−	6.08294e8i		−	1.71963i	0.510608	−	0.859814i	$-0.329420\pi$
$278$		−	6.47514e7i		−	0.180756i
$279$		−	2.87174e7i		−	0.0791644i
$280$	−1.71450e8			−0.466751
$281$		−	4.18125e8i		−	1.12418i	−0.827077	−	0.562088i	$-0.809998\pi$
$281$		−	4.18125e8i		−	1.12418i	0.827077	−	0.562088i	$-0.190002\pi$
$282$			2.32439e8i			0.617217i
$283$		−	3.14375e8i		−	0.824508i	−0.911069	−	0.412254i	$-0.864742\pi$
$283$		−	3.14375e8i		−	0.824508i	0.911069	−	0.412254i	$-0.135258\pi$
$284$	−1.57233e8			−0.407314
$285$	1.16798e9			2.98867
$286$	−7.78606e7			−0.196805
$287$	−2.82357e8			−0.705038
$288$			5.32187e7i			0.131278i
$289$	9.47542e7			0.230917
$290$			2.05849e8i			0.495627i
$291$		−	9.82725e8i		−	2.33779i
$292$	−2.80234e7			−0.0658689
$293$	4.84775e8			1.12591			0.562955	−	0.826487i	$-0.309664\pi$
$293$	4.84775e8			1.12591			0.562955	+	0.826487i	$0.309664\pi$
$294$			2.25215e8i			0.516871i
$295$	8.08329e8			1.83321
$296$	1.57177e8	+	1.34659e7i	0.352263	+	0.0301796i
$297$	−5.46980e7			−0.121150
$298$		−	4.39505e8i		−	0.962070i
$299$	−4.75458e8			−1.02864
$300$	−8.96796e8			−1.91765
$301$			3.60709e8i			0.762386i
$302$			1.19123e8i			0.248870i
$303$	−1.18168e9			−2.44035
$304$		−	1.40296e8i		−	0.286409i
$305$	9.73481e8			1.96462
$306$	−2.30814e8			−0.460508
$307$	2.64014e8			0.520765			0.260383	−	0.965505i	$-0.416151\pi$
$307$	2.64014e8			0.520765			0.260383	+	0.965505i	$0.416151\pi$
$308$	6.10722e7			0.119101
$309$			9.74807e8i			1.87959i
$310$		−	7.81349e7i		−	0.148963i
$311$			7.65348e8i			1.44277i	0.692533	+	0.721386i	$0.256495\pi$
$311$			7.65348e8i			1.44277i	−0.692533	+	0.721386i	$0.743505\pi$
$312$	1.95436e8			0.364303
$313$			2.05467e8i			0.378736i	0.981906	+	0.189368i	$0.0606439\pi$
$313$			2.05467e8i			0.378736i	−0.981906	+	0.189368i	$0.939356\pi$
$314$		−	3.34461e8i		−	0.609665i
$315$		−	5.43855e8i		−	0.980384i
$316$			1.44674e8i			0.257921i
$317$	−7.59668e8			−1.33942			−0.669710	−	0.742623i	$-0.733581\pi$
$317$	−7.59668e8			−1.33942			−0.669710	+	0.742623i	$0.733581\pi$
$318$			3.92013e6i			0.00683605i
$319$		−	7.33251e7i		−	0.126469i
$320$			1.44799e8i			0.247024i
$321$	3.40672e8			0.574869
$322$	3.72939e8			0.622504
$323$	6.08475e8			1.00469
$324$	3.64619e8			0.595568
$325$			1.40345e9i			2.26780i
$326$	7.38987e8			1.18134
$327$		−	6.31580e8i		−	0.998875i
$328$			2.38466e8i			0.373136i
$329$	−2.85323e8			−0.441725
$330$	4.29398e8			0.657751
$331$		−	5.97140e8i		−	0.905062i	−0.891749	−	0.452531i	$-0.850521\pi$
$331$		−	5.97140e8i		−	0.905062i	0.891749	−	0.452531i	$-0.149479\pi$
$332$	−6.21450e8			−0.932015
$333$	−4.27149e7	+	4.98577e8i	−0.0633905	+	0.739908i
$334$	6.08831e7			0.0894096
$335$			1.29451e9i			1.88127i
$336$	−1.53295e8			−0.220466
$337$	−1.32617e9			−1.88753			−0.943764	−	0.330621i	$-0.892742\pi$
$337$	−1.32617e9			−1.88753			−0.943764	+	0.330621i	$0.892742\pi$
$338$			1.96140e8i			0.276285i
$339$			4.19630e8i			0.585016i
$340$	−6.28005e8			−0.866536
$341$			2.78323e7i			0.0380110i
$342$	4.45030e8			0.601586
$343$	−7.75719e8			−1.03795
$344$	3.04638e8			0.403487
$345$	2.62213e9			3.43786
$346$		−	2.78160e8i		−	0.361017i
$347$		−	1.28030e9i		−	1.64497i	−0.568783	−	0.822487i	$-0.692586\pi$
$347$		−	1.28030e9i		−	1.64497i	0.568783	−	0.822487i	$-0.307414\pi$
$348$			1.84051e8i			0.234105i
$349$	−9.62403e8			−1.21190			−0.605952	−	0.795501i	$-0.707208\pi$
$349$	−9.62403e8			−1.21190			−0.605952	+	0.795501i	$0.707208\pi$
$350$		−	1.10083e9i		−	1.37241i
$351$		−	2.14862e8i		−	0.265207i
$352$		−	5.15786e7i		−	0.0630334i
$353$			4.17838e8i			0.505587i	0.967520	+	0.252794i	$0.0813494\pi$
$353$			4.17838e8i			0.505587i	−0.967520	+	0.252794i	$0.918651\pi$
$354$	7.22735e8			0.865899
$355$		−	1.35703e9i		−	1.60986i
$356$			5.59682e8i			0.657456i
$357$		−	6.64855e8i		−	0.773371i
$358$	−3.42063e8			−0.394017
$359$	1.53297e9			1.74865			0.874325	−	0.485341i	$-0.161304\pi$
$359$	1.53297e9			1.74865			0.874325	+	0.485341i	$0.161304\pi$
$360$	−4.59314e8			−0.518861
$361$	−2.79321e8			−0.312485
$362$		−	9.85735e8i		−	1.09214i
$363$	1.05007e9			1.15224
$364$			2.39901e8i			0.260721i
$365$		−	2.41861e8i		−	0.260340i
$366$	8.70398e8			0.927971
$367$	−6.50437e8			−0.686869			−0.343435	−	0.939177i	$-0.611590\pi$
$367$	−6.50437e8			−0.686869			−0.343435	+	0.939177i	$0.611590\pi$
$368$		−	3.14967e8i		−	0.329456i
$369$	−7.56433e8			−0.783751
$370$	−1.16220e8	+	1.35654e9i	−0.119282	+	1.39228i
$371$	−4.81203e6			−0.00489237
$372$		−	6.98611e7i		−	0.0703615i
$373$	−3.42004e8			−0.341232			−0.170616	−	0.985338i	$-0.554576\pi$
$373$	−3.42004e8			−0.341232			−0.170616	+	0.985338i	$0.554576\pi$
$374$	2.23701e8			0.221114
$375$		−	5.07592e9i		−	4.97056i
$376$			2.40971e8i			0.233780i
$377$	2.88032e8			0.276851
$378$			1.68533e8i			0.160496i
$379$	−3.68055e8			−0.347276			−0.173638	−	0.984810i	$-0.555552\pi$
$379$	−3.68055e8			−0.347276			−0.173638	+	0.984810i	$0.555552\pi$
$380$	1.21085e9			1.13200
$381$	2.52439e9			2.33840
$382$	−1.04930e9			−0.963115
$383$			4.90723e8i			0.446315i	0.974782	+	0.223157i	$0.0716364\pi$
$383$			4.90723e8i			0.446315i	−0.974782	+	0.223157i	$0.928364\pi$
$384$			1.29466e8i			0.116680i
$385$			5.27094e8i			0.470734i
$386$	6.84477e8			0.605763
$387$			9.66337e8i			0.847501i
$388$		−	1.01879e9i		−	0.885473i
$389$			1.23564e9i			1.06431i	0.846647	+	0.532154i	$0.178617\pi$
$389$			1.23564e9i			1.06431i	−0.846647	+	0.532154i	$0.821383\pi$
$390$			1.68674e9i			1.43987i
$391$	1.36604e9			1.15570
$392$			2.33481e8i			0.195772i
$393$		−	1.06650e9i		−	0.886314i
$394$			6.92256e8i			0.570204i
$395$	−1.24864e9			−1.01940
$396$	1.63612e8			0.132398
$397$	−1.39163e9			−1.11624			−0.558118	−	0.829762i	$-0.688476\pi$
$397$	−1.39163e9			−1.11624			−0.558118	+	0.829762i	$0.688476\pi$
$398$	−6.79249e8			−0.540055
$399$			1.28190e9i			1.01030i
$400$	−9.29712e8			−0.726337
$401$			7.98885e8i			0.618698i	0.950949	+	0.309349i	$0.100111\pi$
$401$			7.98885e8i			0.618698i	−0.950949	+	0.309349i	$0.899889\pi$
$402$			1.15744e9i			0.888600i
$403$	−1.09330e8			−0.0832090
$404$	−1.22506e9			−0.924317
$405$			3.14691e9i			2.35392i
$406$	−2.25926e8			−0.167543
$407$	4.13985e7	−	4.83212e8i	0.0304371	−	0.355269i
$408$	−5.61505e8			−0.409301
$409$			1.35467e8i			0.0979040i	0.998801	+	0.0489520i	$0.0155881\pi$
$409$			1.35467e8i			0.0979040i	−0.998801	+	0.0489520i	$0.984412\pi$
$410$	−2.05812e9			−1.47478
$411$	−1.63533e9			−1.16187
$412$			1.01059e9i			0.711922i
$413$			8.87170e8i			0.619700i
$414$	9.99100e8			0.692003
$415$		−	5.36354e9i		−	3.68369i
$416$	2.02609e8			0.137985
$417$	4.99671e8			0.337449
$418$	−4.31315e8			−0.288853
$419$	5.81687e8			0.386314			0.193157	−	0.981168i	$-0.438127\pi$
$419$	5.81687e8			0.386314			0.193157	+	0.981168i	$0.438127\pi$
$420$		−	1.32304e9i		−	0.871367i
$421$			8.06048e8i			0.526470i	0.964732	+	0.263235i	$0.0847894\pi$
$421$			8.06048e8i			0.526470i	−0.964732	+	0.263235i	$0.915211\pi$
$422$			1.80483e9i			1.16907i
$423$	−7.64379e8			−0.491041
$424$			4.06401e6i			0.00258925i
$425$		−	4.03224e9i		−	2.54791i
$426$		−	1.21333e9i		−	0.760405i
$427$			1.06843e9i			0.664123i
$428$	3.53176e8			0.217740
$429$		−	6.00833e8i		−	0.367412i
$430$			2.62923e9i			1.59474i
$431$			1.69493e8i			0.101972i	0.998699	+	0.0509860i	$0.0162364\pi$
$431$			1.69493e8i			0.101972i	−0.998699	+	0.0509860i	$0.983764\pi$
$432$	1.42335e8			0.0849412
$433$	−2.67735e9			−1.58489			−0.792443	−	0.609946i	$-0.791191\pi$
$433$	−2.67735e9			−1.58489			−0.792443	+	0.609946i	$0.791191\pi$
$434$	8.57558e7			0.0503558
$435$	−1.58849e9			−0.925276
$436$		−	6.54761e8i		−	0.378338i
$437$	−2.63384e9			−1.50975
$438$		−	2.16250e8i		−	0.122969i
$439$			2.31970e9i			1.30860i	0.756236	+	0.654299i	$0.227036\pi$
$439$			2.31970e9i			1.30860i	−0.756236	+	0.654299i	$0.772964\pi$
$440$	4.45159e8			0.249133
$441$	−7.40622e8			−0.411208
$442$			8.78731e8i			0.484036i
$443$	1.30496e9			0.713155			0.356578	−	0.934266i	$-0.383944\pi$
$443$	1.30496e9			0.713155			0.356578	+	0.934266i	$0.383944\pi$
$444$	−1.03913e8	+	1.21290e9i	−0.0563416	+	0.657632i
$445$	−4.83044e9			−2.59852
$446$		−	1.23098e9i		−	0.657019i
$447$	3.39156e9			1.79607
$448$	−1.58922e8			−0.0835046
$449$		−	1.65924e9i		−	0.865063i	−0.901619	−	0.432531i	$-0.857620\pi$
$449$		−	1.65924e9i		−	0.865063i	0.901619	−	0.432531i	$-0.142380\pi$
$450$		−	2.94912e9i		−	1.52563i
$451$	7.33121e8			0.376320
$452$			4.35032e8i			0.221583i
$453$	−9.19247e8			−0.464610
$454$	4.44843e8			0.223106
$455$	−2.07050e9			−1.03047
$456$	1.08263e9			0.534692
$457$			1.77052e9i			0.867747i	0.900974	+	0.433873i	$0.142853\pi$
$457$			1.77052e9i			0.867747i	−0.900974	+	0.433873i	$0.857147\pi$
$458$			6.02825e8i			0.293199i
$459$			6.17318e8i			0.297965i
$460$	2.71838e9			1.30214
$461$		−	2.09728e9i		−	0.997020i	−0.866884	−	0.498510i	$-0.833881\pi$
$461$		−	2.09728e9i		−	0.997020i	0.866884	−	0.498510i	$-0.166119\pi$
$462$			4.71280e8i			0.222347i
$463$		−	1.22590e9i		−	0.574012i	−0.957929	−	0.287006i	$-0.907340\pi$
$463$		−	1.22590e9i		−	0.574012i	0.957929	−	0.287006i	$-0.0926600\pi$
$464$			1.90806e8i			0.0886707i
$465$	6.02949e8			0.278096
$466$		−	1.51631e9i		−	0.694126i
$467$		−	1.40205e9i		−	0.637022i	−0.947919	−	0.318511i	$-0.896817\pi$
$467$		−	1.40205e9i		−	0.637022i	0.947919	−	0.318511i	$-0.103183\pi$
$468$			6.42692e8i			0.289829i
$469$	−1.42078e9			−0.635946
$470$	−2.07974e9			−0.923988
$471$	2.58096e9			1.13817
$472$	7.49261e8			0.327972
$473$		−	9.36557e8i		−	0.406930i
$474$	−1.11642e9			−0.481507
$475$			7.77451e9i			3.32848i
$476$		−	6.89257e8i		−	0.292925i
$477$	−1.28914e7			−0.00543858
$478$	1.98293e9			0.830443
$479$			8.80464e8i			0.366047i	0.983109	+	0.183024i	$0.0585885\pi$
$479$			8.80464e8i			0.366047i	−0.983109	+	0.183024i	$0.941411\pi$
$480$	−1.11738e9			−0.461165
$481$	1.89813e9	+	1.62619e8i	0.777711	+	0.0666292i
$482$	2.81713e8			0.114589
$483$			2.87789e9i			1.16214i
$484$	1.08861e9			0.436429
$485$	8.79288e9			3.49973
$486$			2.20570e9i			0.871604i
$487$			1.15988e9i			0.455052i	0.973772	+	0.227526i	$0.0730637\pi$
$487$			1.15988e9i			0.455052i	−0.973772	+	0.227526i	$0.926936\pi$
$488$	9.02345e8			0.351482
$489$			5.70259e9i			2.20542i
$490$	−2.01510e9			−0.773768
$491$	2.16496e9			0.825402			0.412701	−	0.910867i	$-0.364585\pi$
$491$	2.16496e9			0.825402			0.412701	+	0.910867i	$0.364585\pi$
$492$	−1.84018e9			−0.696600
$493$	−8.27544e8			−0.311047
$494$		−	1.69427e9i		−	0.632322i
$495$			1.41208e9i			0.523289i
$496$		−	7.24252e7i		−	0.0266504i
$497$	1.48938e9			0.544201
$498$		−	4.79559e9i		−	1.73996i
$499$		−	2.85484e9i		−	1.02856i	−0.857622	−	0.514281i	$-0.828059\pi$
$499$		−	2.85484e9i		−	1.02856i	0.857622	−	0.514281i	$-0.171941\pi$
$500$		−	5.26223e9i		−	1.88267i
$501$			4.69821e8i			0.166917i
$502$	2.30686e9			0.813875
$503$			1.03685e9i			0.363268i	0.983366	+	0.181634i	$0.0581385\pi$
$503$			1.03685e9i			0.363268i	−0.983366	+	0.181634i	$0.941861\pi$
$504$		−	5.04113e8i		−	0.175397i
$505$		−	1.05731e10i		−	3.65326i
$506$	−9.68310e8			−0.332267
$507$	−1.51357e9			−0.515791
$508$	2.61704e9			0.885702
$509$	3.51512e9			1.18148			0.590742	−	0.806861i	$-0.298835\pi$
$509$	3.51512e9			1.18148			0.590742	+	0.806861i	$0.298835\pi$
$510$		−	4.84617e9i		−	1.61772i
$511$	2.65450e8			0.0880056
$512$			1.34218e8i			0.0441942i
$513$		−	1.19024e9i		−	0.389247i
$514$	−1.83539e9			−0.596151
$515$	−8.72204e9			−2.81380
$516$			2.35082e9i			0.753261i
$517$	7.40822e8			0.235775
$518$	−1.48885e9	−	1.27555e8i	−0.470649	−	0.0403221i
$519$	2.14650e9			0.673976
$520$			1.74865e9i			0.545370i
$521$	−3.61049e9			−1.11849			−0.559247	−	0.829001i	$-0.688910\pi$
$521$	−3.61049e9			−1.11849			−0.559247	+	0.829001i	$0.688910\pi$
$522$	−6.05254e8			−0.186248
$523$		−	2.72940e9i		−	0.834280i	−0.908842	−	0.417140i	$-0.863032\pi$
$523$		−	2.72940e9i		−	0.834280i	0.908842	−	0.417140i	$-0.136968\pi$
$524$		−	1.10565e9i		−	0.335704i
$525$	8.49488e9			2.56212
$526$		−	3.74792e9i		−	1.12290i
$527$	3.14114e8			0.0934869
$528$	3.98020e8			0.117676
$529$	−2.50819e9			−0.736657
$530$	−3.50752e7			−0.0102337
$531$			2.37672e9i			0.688886i
$532$			1.32895e9i			0.382664i
$533$			2.87981e9i			0.823794i
$534$	−4.31894e9			−1.22739
$535$			3.04815e9i			0.860592i
$536$			1.19992e9i			0.336570i
$537$		−	2.63962e9i		−	0.735583i
$538$		−	4.46528e8i		−	0.123626i
$539$	7.17798e8			0.197443
$540$			1.22845e9i			0.335721i
$541$			1.07615e9i			0.292203i	0.989270	+	0.146101i	$0.0466726\pi$
$541$			1.07615e9i			0.292203i	−0.989270	+	0.146101i	$0.953327\pi$
$542$		−	7.13652e8i		−	0.192526i
$543$	7.60669e9			2.03890
$544$	−5.82114e8			−0.155029
$545$	5.65103e9			1.49534
$546$	−1.85126e9			−0.486735
$547$			4.54937e9i			1.18849i	0.804284	+	0.594245i	$0.202549\pi$
$547$			4.54937e9i			1.18849i	−0.804284	+	0.594245i	$0.797451\pi$
$548$	−1.69535e9			−0.440076
$549$			2.86231e9i			0.738268i
$550$			2.85824e9i			0.732536i
$551$	1.59558e9			0.406338
$552$	2.43052e9			0.615054
$553$		−	1.37042e9i		−	0.344601i
$554$	4.86635e9			1.21596
$555$	−1.04681e10	−	8.96840e8i	−2.59922	−	0.222684i
$556$	5.18011e8			0.127814
$557$		−	5.70048e8i		−	0.139771i	−0.997555	−	0.0698857i	$-0.977737\pi$
$557$		−	5.70048e8i		−	0.139771i	0.997555	−	0.0698857i	$-0.0222635\pi$
$558$	2.29739e8			0.0559777
$559$	3.67893e9			0.890801
$560$		−	1.37160e9i		−	0.330043i
$561$			1.72625e9i			0.412794i
$562$	3.34500e9			0.794913
$563$		−	2.50929e9i		−	0.592612i	−0.955093	−	0.296306i	$-0.904245\pi$
$563$		−	2.50929e9i		−	0.592612i	0.955093	−	0.296306i	$-0.0957549\pi$
$564$	−1.85951e9			−0.436438
$565$	−3.75462e9			−0.875783
$566$	2.51500e9			0.583015
$567$	−3.45384e9			−0.795722
$568$		−	1.25786e9i		−	0.288014i
$569$			4.96651e9i			1.13021i	0.825019	+	0.565104i	$0.191164\pi$
$569$			4.96651e9i			1.13021i	−0.825019	+	0.565104i	$0.808836\pi$
$570$			9.34384e9i			2.11331i
$571$	−1.22505e9			−0.275378			−0.137689	−	0.990476i	$-0.543967\pi$
$571$	−1.22505e9			−0.275378			−0.137689	+	0.990476i	$0.543967\pi$
$572$		−	6.22885e8i		−	0.139162i
$573$		−	8.09721e9i		−	1.79802i
$574$		−	2.25886e9i		−	0.498537i
$575$			1.74539e10i			3.82874i
$576$	−4.25750e8			−0.0928273
$577$		−	8.35364e9i		−	1.81034i	−0.425048	−	0.905171i	$-0.639743\pi$
$577$		−	8.35364e9i		−	1.81034i	0.425048	−	0.905171i	$-0.360257\pi$
$578$			7.58033e8i			0.163283i
$579$			5.28195e9i			1.13089i
$580$	−1.64679e9			−0.350461
$581$	5.88667e9			1.24524
$582$	7.86180e9			1.65307
$583$	1.24941e7			0.00261135
$584$		−	2.24187e8i		−	0.0465763i
$585$	−5.54686e9			−1.14552
$586$			3.87820e9i			0.796139i
$587$		−	4.56164e9i		−	0.930867i	−0.885083	−	0.465433i	$-0.845899\pi$
$587$		−	4.56164e9i		−	0.930867i	0.885083	−	0.465433i	$-0.154101\pi$
$588$	−1.80172e9			−0.365483
$589$	−6.05640e8			−0.122127
$590$			6.46663e9i			1.29627i
$591$	−5.34198e9			−1.06450
$592$	−1.07727e8	+	1.25741e9i	−0.0213402	+	0.249088i
$593$	−6.46155e9			−1.27246			−0.636232	−	0.771498i	$-0.719508\pi$
$593$	−6.46155e9			−1.27246			−0.636232	+	0.771498i	$0.719508\pi$
$594$		−	4.37584e8i		−	0.0856660i
$595$	5.94876e9			1.15776
$596$	3.51604e9			0.680286
$597$		−	5.24161e9i		−	1.00822i
$598$		−	3.80367e9i		−	0.727358i
$599$	−4.31265e9			−0.819880			−0.409940	−	0.912112i	$-0.634450\pi$
$599$	−4.31265e9			−0.819880			−0.409940	+	0.912112i	$0.634450\pi$
$600$		−	7.17437e9i		−	1.35598i
$601$	−4.13016e9			−0.776079			−0.388039	−	0.921643i	$-0.626848\pi$
$601$	−4.13016e9			−0.776079			−0.388039	+	0.921643i	$0.626848\pi$
$602$	−2.88568e9			−0.539088
$603$	−3.80625e9			−0.706946
$604$	−9.52986e8			−0.175978
$605$			9.39544e9i			1.72494i
$606$		−	9.45347e9i		−	1.72559i
$607$		−	8.72886e9i		−	1.58415i	−0.610421	−	0.792077i	$-0.709000\pi$
$607$		−	8.72886e9i		−	1.58415i	0.610421	−	0.792077i	$-0.291000\pi$
$608$	1.12237e9			0.202522
$609$		−	1.74342e9i		−	0.312782i
$610$			7.78785e9i			1.38919i
$611$			2.91006e9i			0.516128i
$612$		−	1.84651e9i		−	0.325629i
$613$	−6.95813e9			−1.22006			−0.610030	−	0.792378i	$-0.708843\pi$
$613$	−6.95813e9			−1.22006			−0.610030	+	0.792378i	$0.708843\pi$
$614$			2.11211e9i			0.368237i
$615$		−	1.58820e10i		−	2.75324i
$616$			4.88577e8i			0.0842172i
$617$	7.38172e9			1.26520			0.632601	−	0.774478i	$-0.281987\pi$
$617$	7.38172e9			1.26520			0.632601	+	0.774478i	$0.281987\pi$
$618$	−7.79845e9			−1.32907
$619$	8.15556e9			1.38209			0.691045	−	0.722811i	$-0.257150\pi$
$619$	8.15556e9			1.38209			0.691045	+	0.722811i	$0.257150\pi$
$620$	6.25079e8			0.105333
$621$		−	2.67212e9i		−	0.447750i
$622$	−6.12278e9			−1.02019
$623$		−	5.30158e9i		−	0.878409i
$624$			1.56348e9i			0.257601i
$625$	2.76837e10			4.53570
$626$	−1.64374e9			−0.267807
$627$		−	3.32836e9i		−	0.539255i
$628$	2.67569e9			0.431098
$629$	−5.45351e9	−	4.67221e8i	−0.873773	−	0.0748591i
$630$	4.35084e9			0.693236
$631$		−	5.34604e9i		−	0.847090i	−0.905875	−	0.423545i	$-0.860785\pi$
$631$		−	5.34604e9i		−	0.847090i	0.905875	−	0.423545i	$-0.139215\pi$
$632$	−1.15739e9			−0.182378
$633$	−1.39274e10			−2.18252
$634$		−	6.07735e9i		−	0.947112i
$635$			2.25868e10i			3.50064i
$636$	−3.13610e7			−0.00483382
$637$			2.81962e9i			0.432217i
$638$	5.86601e8			0.0894274
$639$	3.99005e9			0.604958
$640$	−1.15839e9			−0.174673
$641$	−4.54936e9			−0.682256			−0.341128	−	0.940017i	$-0.610809\pi$
$641$	−4.54936e9			−0.682256			−0.341128	+	0.940017i	$0.610809\pi$
$642$			2.72538e9i			0.406494i
$643$		−	3.88181e9i		−	0.575833i	−0.957656	−	0.287916i	$-0.907038\pi$
$643$		−	3.88181e9i		−	0.575833i	0.957656	−	0.287916i	$-0.0929625\pi$
$644$			2.98351e9i			0.440177i
$645$	−2.02892e10			−2.97718
$646$			4.86780e9i			0.710426i
$647$			1.86109e9i			0.270149i	0.990835	+	0.135075i	$0.0431274\pi$
$647$			1.86109e9i			0.270149i	−0.990835	+	0.135075i	$0.956873\pi$
$648$			2.91695e9i			0.421130i
$649$		−	2.30347e9i		−	0.330770i
$650$	−1.12276e10			−1.60358
$651$			6.61757e8i			0.0940081i
$652$			5.91190e9i			0.835334i
$653$		−	3.38262e9i		−	0.475398i	−0.971339	−	0.237699i	$-0.923607\pi$
$653$		−	3.38262e9i		−	0.475398i	0.971339	−	0.237699i	$-0.0763931\pi$
$654$	5.05264e9			0.706311
$655$	9.54247e9			1.32683
$656$	−1.90773e9			−0.263847
$657$	7.11140e8			0.0978309
$658$		−	2.28259e9i		−	0.312347i
$659$	−8.75702e9			−1.19195			−0.595974	−	0.803004i	$-0.703234\pi$
$659$	−8.75702e9			−1.19195			−0.595974	+	0.803004i	$0.703234\pi$
$660$			3.43519e9i			0.465100i
$661$			4.74653e9i			0.639250i	0.947544	+	0.319625i	$0.103557\pi$
$661$			4.74653e9i			0.639250i	−0.947544	+	0.319625i	$0.896443\pi$
$662$	4.77712e9			0.639975
$663$	−6.78096e9			−0.903637
$664$		−	4.97160e9i		−	0.659034i
$665$	−1.14697e10			−1.51244
$666$	−3.98862e9	−	3.41719e8i	−0.523194	−	0.0448238i
$667$	3.58210e9			0.467409
$668$			4.87065e8i			0.0632222i
$669$	9.49917e9			1.22657
$670$	−1.03561e10			−1.33026
$671$		−	2.77410e9i		−	0.354482i
$672$		−	1.22636e9i		−	0.155893i
$673$	1.91258e9			0.241862			0.120931	−	0.992661i	$-0.461412\pi$
$673$	1.91258e9			0.241862			0.120931	+	0.992661i	$0.461412\pi$
$674$		−	1.06093e10i		−	1.33468i
$675$	−7.88751e9			−0.987135
$676$	−1.56912e9			−0.195363
$677$	3.73391e9			0.462491			0.231245	−	0.972895i	$-0.425720\pi$
$677$	3.73391e9			0.462491			0.231245	+	0.972895i	$0.425720\pi$
$678$	−3.35704e9			−0.413669
$679$			9.65049e9i			1.18306i
$680$		−	5.02404e9i		−	0.612733i
$681$			3.43275e9i			0.416512i
$682$	−2.22659e8			−0.0268778
$683$			5.24953e8i			0.0630446i	0.999503	+	0.0315223i	$0.0100355\pi$
$683$			5.24953e8i			0.0630446i	−0.999503	+	0.0315223i	$0.989964\pi$
$684$			3.56024e9i			0.425386i
$685$		−	1.46320e10i		−	1.73935i
$686$		−	6.20575e9i		−	0.733939i
$687$	−4.65186e9			−0.547366
$688$			2.43710e9i			0.285308i
$689$			4.90787e7i			0.00571644i
$690$			2.09771e10i			2.43093i
$691$	−5.79537e8			−0.0668202			−0.0334101	−	0.999442i	$-0.510637\pi$
$691$	−5.79537e8			−0.0668202			−0.0334101	+	0.999442i	$0.510637\pi$
$692$	2.22528e9			0.255278
$693$	−1.54981e9			−0.176893
$694$	1.02424e10			1.16317
$695$			4.47079e9i			0.505169i
$696$	−1.47241e9			−0.165537
$697$		−	8.27396e9i		−	0.925548i
$698$		−	7.69922e9i		−	0.856945i
$699$	1.17010e10			1.29585
$700$	8.80667e9			0.970440
$701$			5.58220e9i			0.612058i	0.952022	+	0.306029i	$0.0990004\pi$
$701$			5.58220e9i			0.612058i	−0.952022	+	0.306029i	$0.901000\pi$
$702$	1.71889e9			0.187529
$703$	1.05148e10	+	9.00843e8i	1.14146	+	0.0977925i
$704$	4.12629e8			0.0445713
$705$		−	1.60489e10i		−	1.72497i
$706$	−3.34270e9			−0.357504
$707$	1.16043e10			1.23496
$708$			5.78188e9i			0.612283i
$709$		−	5.62005e9i		−	0.592214i	−0.955155	−	0.296107i	$-0.904312\pi$
$709$		−	5.62005e9i		−	0.592214i	0.955155	−	0.296107i	$-0.0956885\pi$
$710$	1.08562e10			1.13835
$711$		−	3.67135e9i		−	0.383074i
$712$	−4.47746e9			−0.464891
$713$	−1.35967e9			−0.140482
$714$	5.31884e9			0.546856
$715$	5.37592e9			0.550024
$716$		−	2.73650e9i		−	0.278612i
$717$			1.53018e10i			1.55034i
$718$			1.22638e10i			1.23648i
$719$	4.72956e8			0.0474536			0.0237268	−	0.999718i	$-0.492447\pi$
$719$	4.72956e8			0.0474536			0.0237268	+	0.999718i	$0.492447\pi$
$720$		−	3.67451e9i		−	0.366890i
$721$		−	9.57274e9i		−	0.951180i
$722$		−	2.23457e9i		−	0.220960i
$723$			2.17392e9i			0.213924i
$724$	7.88588e9			0.772263
$725$		−	1.05736e10i		−	1.03048i
$726$			8.40055e9i			0.814760i
$727$			9.56076e9i			0.922830i	0.887184	+	0.461415i	$0.152658\pi$
$727$			9.56076e9i			0.922830i	−0.887184	+	0.461415i	$0.847342\pi$
$728$	−1.91920e9			−0.184358
$729$	−4.56116e9			−0.436043
$730$	1.93488e9			0.184088
$731$	−1.05699e10			−1.00083
$732$			6.96319e9i			0.656174i
$733$	−7.81007e9			−0.732472			−0.366236	−	0.930522i	$-0.619354\pi$
$733$	−7.81007e9			−0.732472			−0.366236	+	0.930522i	$0.619354\pi$
$734$		−	5.20350e9i		−	0.485690i
$735$		−	1.55501e10i		−	1.44453i
$736$	2.51973e9			0.232960
$737$	3.68894e9			0.339442
$738$		−	6.05146e9i		−	0.554196i
$739$	1.10335e9			0.100568			0.0502839	−	0.998735i	$-0.483987\pi$
$739$	1.10335e9			0.100568			0.0502839	+	0.998735i	$0.483987\pi$
$740$	−1.08523e10	−	9.29756e8i	−0.984491	−	0.0843448i
$741$	1.30743e10			1.18047
$742$		−	3.84962e7i		−	0.00345943i
$743$	−1.08055e9			−0.0966462			−0.0483231	−	0.998832i	$-0.515388\pi$
$743$	−1.08055e9			−0.0966462			−0.0483231	+	0.998832i	$0.515388\pi$
$744$	5.58889e8			0.0497531
$745$			3.03458e10i			2.68876i
$746$		−	2.73603e9i		−	0.241288i
$747$	1.57703e10			1.38426
$748$			1.78961e9i			0.156352i
$749$	−3.34545e9			−0.290916
$750$	4.06074e10			3.51472
$751$	−2.96287e9			−0.255254			−0.127627	−	0.991822i	$-0.540736\pi$
$751$	−2.96287e9			−0.255254			−0.127627	+	0.991822i	$0.540736\pi$
$752$	−1.92776e9			−0.165307
$753$			1.78015e10i			1.51941i
$754$			2.30426e9i			0.195763i
$755$		−	8.22492e9i		−	0.695532i
$756$	−1.34826e9			−0.113488
$757$		−	2.08894e10i		−	1.75021i	−0.483932	−	0.875106i	$-0.660792\pi$
$757$		−	2.08894e10i		−	1.75021i	0.483932	−	0.875106i	$-0.339208\pi$
$758$		−	2.94444e9i		−	0.245561i
$759$		−	7.47223e9i		−	0.620303i
$760$			9.68678e9i			0.800446i
$761$	8.64924e9			0.711429			0.355715	−	0.934595i	$-0.384237\pi$
$761$	8.64924e9			0.711429			0.355715	+	0.934595i	$0.384237\pi$
$762$			2.01951e10i			1.65350i
$763$			6.20220e9i			0.505487i
$764$		−	8.39440e9i		−	0.681025i
$765$	1.59367e10			1.28701
$766$	−3.92579e9			−0.315592
$767$	9.04839e9			0.724081
$768$	−1.03573e9			−0.0825052
$769$			8.78340e9i			0.696499i	0.937402	+	0.348249i	$0.113224\pi$
$769$			8.78340e9i			0.696499i	−0.937402	+	0.348249i	$0.886776\pi$
$770$	−4.21675e9			−0.332859
$771$		−	1.41633e10i		−	1.11294i
$772$			5.47581e9i			0.428339i
$773$	−1.50852e10			−1.17469			−0.587343	−	0.809338i	$-0.699826\pi$
$773$	−1.50852e10			−1.17469			−0.587343	+	0.809338i	$0.699826\pi$
$774$	−7.73070e9			−0.599274
$775$			4.01345e9i			0.309715i
$776$	8.15035e9			0.626124
$777$	9.84313e8	−	1.14891e10i	0.0752765	−	0.878645i
$778$	−9.88510e9			−0.752580
$779$			1.59529e10i			1.20909i
$780$	−1.34939e10			−1.01814
$781$	−3.86708e9			−0.290472
$782$			1.09283e10i			0.817201i
$783$			1.61877e9i			0.120509i
$784$	−1.86785e9			−0.138432
$785$			2.30930e10i			1.70387i
$786$	8.53201e9			0.626719
$787$	6.04283e9			0.441905			0.220953	−	0.975285i	$-0.429083\pi$
$787$	6.04283e9			0.441905			0.220953	+	0.975285i	$0.429083\pi$
$788$	−5.53805e9			−0.403195
$789$	2.89219e10			2.09632
$790$		−	9.98910e9i		−	0.720828i
$791$		−	4.12083e9i		−	0.296051i
$792$			1.30889e9i			0.0936195i
$793$	1.08971e10			0.775987
$794$		−	1.11330e10i		−	0.789298i
$795$		−	2.70667e8i		−	0.0191051i
$796$		−	5.43399e9i		−	0.381877i
$797$		−	2.37936e10i		−	1.66477i	−0.554194	−	0.832387i	$-0.686974\pi$
$797$		−	2.37936e10i		−	1.66477i	0.554194	−	0.832387i	$-0.313026\pi$
$798$	−1.02552e10			−0.714387
$799$		−	8.36088e9i		−	0.579880i
$800$		−	7.43769e9i		−	0.513598i
$801$		−	1.42029e10i		−	0.976478i
$802$	−6.39108e9			−0.437486
$803$	−6.89223e8			−0.0469738
$804$	−9.25950e9			−0.628335
$805$	−2.57497e10			−1.73975
$806$		−	8.74637e8i		−	0.0588376i
$807$	3.44575e9			0.230795
$808$		−	9.80045e9i		−	0.653591i
$809$		−	2.96588e9i		−	0.196940i	−0.995140	−	0.0984699i	$-0.968605\pi$
$809$		−	2.96588e9i		−	0.196940i	0.995140	−	0.0984699i	$-0.0313948\pi$
$810$	−2.51753e10			−1.66447
$811$	9.96442e9			0.655963			0.327981	−	0.944684i	$-0.393632\pi$
$811$	9.96442e9			0.655963			0.327981	+	0.944684i	$0.393632\pi$
$812$		−	1.80741e9i		−	0.118470i
$813$	5.50709e9			0.359422
$814$	3.86570e9	+	3.31188e8i	0.251213	+	0.0215223i
$815$	−5.10237e10			−3.30157
$816$		−	4.49204e9i		−	0.289420i
$817$	2.03798e10			1.30744
$818$	−1.08373e9			−0.0692286
$819$		−	6.08788e9i		−	0.387233i
$820$		−	1.64650e10i		−	1.04283i
$821$	−2.00078e10			−1.26182			−0.630910	−	0.775856i	$-0.717318\pi$
$821$	−2.00078e10			−1.26182			−0.630910	+	0.775856i	$0.717318\pi$
$822$		−	1.30826e10i		−	0.821569i
$823$	−2.93972e10			−1.83826			−0.919128	−	0.393960i	$-0.871105\pi$
$823$	−2.93972e10			−1.83826			−0.919128	+	0.393960i	$0.871105\pi$
$824$	−8.08468e9			−0.503405
$825$	−2.20564e10			−1.36756
$826$	−7.09736e9			−0.438194
$827$		−	4.87011e9i		−	0.299412i	−0.988731	−	0.149706i	$-0.952167\pi$
$827$		−	4.87011e9i		−	0.299412i	0.988731	−	0.149706i	$-0.0478327\pi$
$828$			7.99280e9i			0.489320i
$829$			1.38134e10i			0.842091i	0.907040	+	0.421045i	$0.138337\pi$
$829$			1.38134e10i			0.842091i	−0.907040	+	0.421045i	$0.861663\pi$
$830$	4.29083e10			2.60476
$831$			3.75525e10i			2.27005i
$832$			1.62087e9i			0.0975700i
$833$		−	8.10102e9i		−	0.485604i
$834$			3.99737e9i			0.238613i
$835$	−4.20370e9			−0.249879
$836$		−	3.45052e9i		−	0.204250i
$837$		−	6.14443e8i		−	0.0362195i
$838$			4.65350e9i			0.273165i
$839$	7.72042e9			0.451309			0.225654	−	0.974207i	$-0.427548\pi$
$839$	7.72042e9			0.451309			0.225654	+	0.974207i	$0.427548\pi$
$840$	1.05843e10			0.616150
$841$	1.50798e10			0.874200
$842$	−6.44838e9			−0.372270
$843$			2.58126e10i			1.48401i
$844$	−1.44386e10			−0.826660
$845$		−	1.35426e10i		−	0.772151i
$846$		−	6.11503e9i		−	0.347218i
$847$	−1.03118e10			−0.583101
$848$	−3.25121e7			−0.00183088
$849$			1.94076e10i			1.08842i
$850$	3.22579e10			1.80165
$851$	2.36060e10	+	2.02241e9i	1.31301	+	0.112490i
$852$	9.70664e9			0.537688
$853$		−	3.58209e9i		−	0.197613i	−0.995107	−	0.0988063i	$-0.968498\pi$
$853$		−	3.58209e9i		−	0.197613i	0.995107	−	0.0988063i	$-0.0315024\pi$
$854$	−8.54744e9			−0.469606
$855$	−3.07273e10			−1.68129
$856$			2.82541e9i			0.153965i
$857$		−	3.33804e10i		−	1.81158i	−0.423723	−	0.905792i	$-0.639277\pi$
$857$		−	3.33804e10i		−	1.81158i	0.423723	−	0.905792i	$-0.360723\pi$
$858$	4.80666e9			0.259799
$859$		−	2.49538e10i		−	1.34326i	−0.740886	−	0.671630i	$-0.765594\pi$
$859$		−	2.49538e10i		−	1.34326i	0.740886	−	0.671630i	$-0.234406\pi$
$860$	−2.10339e10			−1.12765
$861$	1.74311e10			0.930709
$862$	−1.35594e9			−0.0721051
$863$	4.38135e9			0.232044			0.116022	−	0.993247i	$-0.462986\pi$
$863$	4.38135e9			0.232044			0.116022	+	0.993247i	$0.462986\pi$
$864$			1.13868e9i			0.0600625i
$865$			1.92057e10i			1.00896i
$866$		−	2.14188e10i		−	1.12068i
$867$	−5.84957e9			−0.304829
$868$			6.86046e8i			0.0356069i
$869$			3.55821e9i			0.183934i
$870$		−	1.27079e10i		−	0.654269i
$871$			1.44907e10i			0.743065i
$872$	5.23809e9			0.267525
$873$			2.58536e10i			1.31514i
$874$		−	2.10707e10i		−	1.06755i
$875$			4.98463e10i			2.51539i
$876$	1.73000e9			0.0869524
$877$	3.48494e10			1.74460			0.872302	−	0.488967i	$-0.162626\pi$
$877$	3.48494e10			1.74460			0.872302	+	0.488967i	$0.162626\pi$
$878$	−1.85576e10			−0.925319
$879$	−2.99272e10			−1.48630
$880$			3.56127e9i			0.176163i
$881$	1.70363e10			0.839382			0.419691	−	0.907667i	$-0.362138\pi$
$881$	1.70363e10			0.839382			0.419691	+	0.907667i	$0.362138\pi$
$882$		−	5.92498e9i		−	0.290768i
$883$			2.78803e10i			1.36281i	0.731907	+	0.681404i	$0.238630\pi$
$883$			2.78803e10i			1.36281i	−0.731907	+	0.681404i	$0.761370\pi$
$884$	−7.02985e9			−0.342265
$885$	−4.99015e10			−2.41998
$886$			1.04397e10i			0.504277i
$887$	6.16592e8			0.0296664			0.0148332	−	0.999890i	$-0.495278\pi$
$887$	6.16592e8			0.0296664			0.0148332	+	0.999890i	$0.495278\pi$
$888$	−9.70317e9	−	8.31304e8i	−0.465016	−	0.0398396i
$889$	−2.47899e10			−1.18336
$890$		−	3.86435e10i		−	1.83743i
$891$	8.96765e9			0.424724
$892$	9.84781e9			0.464583
$893$			1.61205e10i			0.757528i
$894$			2.71325e10i			1.27001i
$895$	2.36179e10			1.10119
$896$		−	1.27137e9i		−	0.0590466i
$897$	2.93520e10			1.35789
$898$	1.32739e10			0.611692
$899$	8.23688e8			0.0378098
$900$	2.35930e10			1.07878
$901$		−	1.41008e8i		−	0.00642253i
$902$			5.86497e9i			0.266099i
$903$		−	2.22681e10i		−	1.00641i
$904$	−3.48025e9			−0.156683
$905$			6.80605e10i			3.05228i
$906$		−	7.35398e9i		−	0.328529i
$907$			3.96059e10i			1.76252i	0.472632	+	0.881260i	$0.343304\pi$
$907$			3.96059e10i			1.76252i	−0.472632	+	0.881260i	$0.656696\pi$
$908$			3.55875e9i			0.157760i
$909$	3.10878e10			1.37283
$910$		−	1.65640e10i		−	0.728654i
$911$		−	3.43997e10i		−	1.50744i	−0.657195	−	0.753721i	$-0.728257\pi$
$911$		−	3.43997e10i		−	1.50744i	0.657195	−	0.753721i	$-0.271743\pi$
$912$			8.66104e9i			0.378084i
$913$	−1.52843e10			−0.664658
$914$	−1.41641e10			−0.613590
$915$	−6.00970e10			−2.59346
$916$	−4.82260e9			−0.207323
$917$			1.04732e10i			0.448525i
$918$	−4.93855e9			−0.210693
$919$		−	2.27101e10i		−	0.965193i	−0.875843	−	0.482597i	$-0.839694\pi$
$919$		−	2.27101e10i		−	0.965193i	0.875843	−	0.482597i	$-0.160306\pi$
$920$			2.17470e10i			0.920751i
$921$	−1.62987e10			−0.687454
$922$	1.67783e10			0.704999
$923$		−	1.51905e10i		−	0.635865i
$924$	−3.77024e9			−0.157223
$925$	5.96970e9	−	6.96797e10i	0.248003	−	2.89474i
$926$	9.80719e9			0.405888
$927$		−	2.56453e10i		−	1.05737i
$928$	−1.52645e9			−0.0626996
$929$	1.05933e9			0.0433486			0.0216743	−	0.999765i	$-0.493100\pi$
$929$	1.05933e9			0.0433486			0.0216743	+	0.999765i	$0.493100\pi$
$930$			4.82359e9i			0.196644i
$931$			1.56195e10i			0.634370i
$932$	1.21305e10			0.490821
$933$		−	4.72481e10i		−	1.90458i
$934$	1.12164e10			0.450442
$935$	−1.54455e10			−0.617962
$936$	−5.14153e9			−0.204940
$937$	−3.30467e10			−1.31232			−0.656159	−	0.754623i	$-0.727820\pi$
$937$	−3.30467e10			−1.31232			−0.656159	+	0.754623i	$0.727820\pi$
$938$		−	1.13662e10i		−	0.449682i
$939$		−	1.26843e10i		−	0.499963i
$940$		−	1.66379e10i		−	0.653358i
$941$	−4.15251e9			−0.162460			−0.0812301	−	0.996695i	$-0.525885\pi$
$941$	−4.15251e9			−0.162460			−0.0812301	+	0.996695i	$0.525885\pi$
$942$			2.06477e10i			0.804809i
$943$			3.58146e10i			1.39082i
$944$			5.99409e9i			0.231911i
$945$		−	1.16364e10i		−	0.448547i
$946$	7.49245e9			0.287743
$947$			4.40593e10i			1.68583i	0.538049	+	0.842913i	$0.319161\pi$
$947$			4.40593e10i			1.68583i	−0.538049	+	0.842913i	$0.680839\pi$
$948$		−	8.93135e9i		−	0.340477i
$949$		−	2.70737e9i		−	0.102829i
$950$	−6.21961e10			−2.35359
$951$	4.68975e10			1.76814
$952$	5.51406e9			0.207129
$953$	−1.60804e10			−0.601827			−0.300913	−	0.953651i	$-0.597292\pi$
$953$	−1.60804e10			−0.601827			−0.300913	+	0.953651i	$0.597292\pi$
$954$		−	1.03131e8i		−	0.00384565i
$955$	7.24494e10			2.69168
$956$			1.58634e10i			0.587212i
$957$			4.52667e9i			0.166950i
$958$	−7.04371e9			−0.258835
$959$	1.60592e10			0.587974
$960$		−	8.93903e9i		−	0.326093i
$961$	2.72000e10			0.988636
$962$	−1.30095e9	+	1.51850e10i	−0.0471139	+	0.549925i
$963$	−8.96242e9			−0.323395
$964$			2.25370e9i			0.0810266i
$965$	−4.72600e10			−1.69296
$966$	−2.30231e10			−0.821757
$967$		−	3.17212e10i		−	1.12813i	−0.825732	−	0.564063i	$-0.809238\pi$
$967$		−	3.17212e10i		−	1.12813i	0.825732	−	0.564063i	$-0.190762\pi$
$968$			8.70888e9i			0.308602i
$969$	−3.75637e10			−1.32628
$970$			7.03430e10i			2.47469i
$971$	3.30660e10			1.15908			0.579540	−	0.814944i	$-0.303232\pi$
$971$	3.30660e10			1.15908			0.579540	+	0.814944i	$0.303232\pi$
$972$	−1.76456e10			−0.616317
$973$	−4.90685e9			−0.170768
$974$	−9.27903e9			−0.321770
$975$		−	8.66407e10i		−	2.99368i
$976$			7.21876e9i			0.248535i
$977$			1.35605e10i			0.465206i	0.972572	+	0.232603i	$0.0747243\pi$
$977$			1.35605e10i			0.465206i	−0.972572	+	0.232603i	$0.925276\pi$
$978$	−4.56207e10			−1.55947
$979$			1.37652e10i			0.468859i
$980$		−	1.61208e10i		−	0.547137i
$981$			1.66157e10i			0.561922i
$982$			1.73197e10i			0.583647i
$983$	1.33447e10			0.448095			0.224048	−	0.974578i	$-0.428073\pi$
$983$	1.33447e10			0.448095			0.224048	+	0.974578i	$0.428073\pi$
$984$		−	1.47215e10i		−	0.492571i
$985$		−	4.77971e10i		−	1.59358i
$986$		−	6.62035e9i		−	0.219944i
$987$	1.76142e10			0.583113
$988$	1.35542e10			0.447119
$989$	4.57529e10			1.50394
$990$	−1.12966e10			−0.370021
$991$		−	3.89565e10i		−	1.27152i	−0.771888	−	0.635758i	$-0.780688\pi$
$991$		−	3.89565e10i		−	1.27152i	0.771888	−	0.635758i	$-0.219312\pi$
$992$	5.79402e8			0.0188447
$993$			3.68639e10i			1.19476i
$994$			1.19151e10i			0.384808i
$995$	4.68990e10			1.50933
$996$	3.83647e10			1.23034
$997$		−	6.34894e9i		−	0.202894i	−0.994841	−	0.101447i	$-0.967653\pi$
$997$		−	6.34894e9i		−	0.202894i	0.994841	−	0.101447i	$-0.0323472\pi$
$998$	2.28387e10			0.727303
$999$	−9.13936e8	+	1.06677e10i	−0.0290026	+	0.338525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.b.a.73.14	yes	24
37.36	even	2	inner	74.8.b.a.73.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.b.a.73.2	✓	24	37.36	even	2	inner
74.8.b.a.73.14	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+8.00000i q^{2} -61.7342 q^{3} -64.0000 q^{4} -552.363i q^{5} -493.873i q^{6} +606.238 q^{7} -512.000i q^{8} +1624.11 q^{9} +4418.91 q^{10} -1574.05 q^{11} +3950.99 q^{12} -6183.12i q^{13} +4849.91i q^{14} +34099.7i q^{15} +4096.00 q^{16} +17764.7i q^{17} +12992.9i q^{18} -34251.9i q^{19} +35351.3i q^{20} -37425.6 q^{21} -12592.4i q^{22} -76896.1i q^{23} +31607.9i q^{24} -226980. q^{25} +49465.0 q^{26} +34749.7 q^{27} -38799.3 q^{28} +46583.6i q^{29} -272798. q^{30} -17681.9i q^{31} +32768.0i q^{32} +97173.0 q^{33} -142118. q^{34} -334864. i q^{35} -103943. q^{36} +(-26300.5 + 306986. i) q^{37} +274015. q^{38} +381710. i q^{39} -282810. q^{40} -465753. q^{41} -299405. i q^{42} +594996. i q^{43} +100740. q^{44} -897097. i q^{45} +615169. q^{46} -470646. q^{47} -252863. q^{48} -456018. q^{49} -1.81584e6i q^{50} -1.09669e6i q^{51} +395720. i q^{52} -7937.52 q^{53} +277998. i q^{54} +869450. i q^{55} -310394. i q^{56} +2.11451e6i q^{57} -372669. q^{58} +1.46340e6i q^{59} -2.18238e6i q^{60} +1.76239e6i q^{61} +141456. q^{62} +984596. q^{63} -262144. q^{64} -3.41533e6 q^{65} +777384. i q^{66} -2.34359e6 q^{67} -1.13694e6i q^{68} +4.74712e6i q^{69} +2.67891e6 q^{70} +2.45676e6 q^{71} -831543. i q^{72} +437865. q^{73} +(-2.45588e6 - 210404. i) q^{74} +1.40124e7 q^{75} +2.19212e6i q^{76} -954252. q^{77} -3.05368e6 q^{78} -2.26054e6i q^{79} -2.26248e6i q^{80} -5.69717e6 q^{81} -3.72603e6i q^{82} +9.71016e6 q^{83} +2.39524e6 q^{84} +9.81257e6 q^{85} -4.75997e6 q^{86} -2.87580e6i q^{87} +805916. i q^{88} -8.74504e6i q^{89} +7.17678e6 q^{90} -3.74845e6i q^{91} +4.92135e6i q^{92} +1.09158e6i q^{93} -3.76517e6i q^{94} -1.89195e7 q^{95} -2.02291e6i q^{96} +1.59186e7i q^{97} -3.64815e6i q^{98} -2.55643e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 106 q^{3} - 1536 q^{4} + 104 q^{7} + 17554 q^{9} + 1136 q^{10} + 366 q^{11} + 6784 q^{12} + 98304 q^{16} - 239820 q^{21} - 675570 q^{25} + 97008 q^{26} + 338780 q^{27} - 6656 q^{28} + 350400 q^{30}+ \cdots - 53279900 q^{99}+O(q^{100}) \) 24 * q - 106 * q^3 - 1536 * q^4 + 104 * q^7 + 17554 * q^9 + 1136 * q^10 + 366 * q^11 + 6784 * q^12 + 98304 * q^16 - 239820 * q^21 - 675570 * q^25 + 97008 * q^26 + 338780 * q^27 - 6656 * q^28 + 350400 * q^30 - 763792 * q^33 + 713632 * q^34 - 1123456 * q^36 + 41652 * q^37 - 30816 * q^38 - 72704 * q^40 + 1729722 * q^41 - 23424 * q^44 - 488496 * q^46 + 114756 * q^47 - 434176 * q^48 + 4003056 * q^49 - 1115964 * q^53 - 2075632 * q^58 + 3248208 * q^62 - 2350900 * q^63 - 6291456 * q^64 - 5246556 * q^65 - 2717994 * q^67 - 5649440 * q^70 + 10643280 * q^71 - 10450370 * q^73 - 1064064 * q^74 - 17737980 * q^75 + 11665236 * q^77 + 8431856 * q^78 + 47300176 * q^81 + 555912 * q^83 + 15348480 * q^84 - 4853096 * q^85 - 12070464 * q^86 + 32064160 * q^90 - 58516956 * q^95 - 53279900 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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